## amelapal 2 years ago 4 sin^4 x + 3sin^2 x - 1 = 0 After I borrow the 4 I just don't know what to do afterwords..

1. Iamgmg90

let sin^2x = u, substitute and solve as a quadratic? i.e 4u^2 + 3u - 1 = (4u - 1)(u + 1 ) so u = 1/4 or -1, therefore sin^2(x) = 1/4 or -1, use calculator

2. Iamgmg90

sin^-1(SQRT(1/4) = sin^-1(1/2)

3. amelapal

Can the quadratic formula be used if its to the 4th degree because I got the same thing, however I used factoring with borrow and payback.

4. ByteMe

Yes... you can use the QF but I think factoring, as shown above is faster...

5. ByteMe

Also, $$\large sin^2x=\frac{1}{4}$$ gives $$\large sinx=\pm \frac{1}{2}$$ so you'll need to solve sinx=1/2, and also sinx=-1/2

6. Iamgmg90

Oh, thanks. Yes square rooting yields both signs, as squaring makes positive (negative time negative). The -1 can be ignored as it would be a complex number

7. ByteMe

yep...

8. amelapal

So the angles would be 30 and 150, and 210 and 330?

9. amelapal

The other one would come up with i so is it okay to ignore it since it is complex?